Comparison of the Identifiability of Flow Curves from the Hydraulic Bulge Test by Membrane Theory and Inverse Analysis

Abstract:

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In the hydraulic bulge test, flow curves are determined by applying a hydrostatic pressure to one side of a clamped sheet metal specimen, which bulges freely into a circular cavity under the pressure. The pressure and various data such as bulge height, curvature and equivalent strain at the pole are recorded and used to calculate the flow curve of the specimen material using analytical equations based on membrane theory. In the determination of the flow curve, the elastic behavior of the specimen, the elastic-plastic transition and bending effects are neglected, and the flow curves calculated this way are affected by these simplifications. An alternative to this procedure is an inverse analysis, which proceeds by searching for a flow curve that minimizes the difference between computed and measured data, e.g. bulge height vs. pressure. An inverse analysis based on a finite element model takes into account elastic and bending effects but since it involves the solution of an optimization problem, it is not clear whether it yields more accurate results than membrane theory. The objective of this paper is to compare the ‘identifiability’ of a given flow curve from the bulge test by direct identification based on membrane theory and by inverse analysis with different objective functions to be minimized. Using a re-identification procedure, it is shown that an inverse analysis can improve the results of the direct identification if a suitable objective function is chosen.

Abstract: This work covers the finite element analysis of geometric and process parameters in hydraulic bulge tests in terms of the accuracy of the evaluated flow curve. The important parameters are identified and varied to cover the whole range of possible uses. The effects of these parameters are analyzed for three representative materials: aluminium, mid-strength steel, and high-strength steel. The flow curves of the materials for each set of parameters are calculated by using the results of the simulations and the membrane theory. It is seen that even with simulation results, it is not always possible to obtain the input flow curve, especially towards the end of the test. The dimensions of the sheet and the tooling affect the plastic strain development and geometry of the bulge, leading to errors in computed flow curves. In order to observe the effect of the material flow from the flange on the determined yield stresses, the function and position of the drawbeads are also examined. These parameters, together with the method used to calculate the radius of the bulge, determine the accuracy of the calculated flow curve. Guidelines for an accurate flow curve determination regarding the test set-up and calculation methods are given.

Abstract: The standard uniaxial tensile test is the widely accepted method to obtain relevant properties of mechanical characterization of sheet metal materials. However the range of strain obtained from tensile test is limited. The bulge test is an alternative to obtain ranges of deformation, higher than tensile test, thus permitting a better characterization for material behaviour. This paper presents a sensitivity analysis for some influencing variables used in bulge measurements, thus giving some guidelines for the evaluation of the stress-strain curve from experimental results using a developed experimental mechanical system. Additionally, using bulge test up to fracture shall give material information regarding damage, which in turn may be used to evaluate and calibrate damage models. A methodology is presented to be used for evaluation and calibration of Ito-Goya damage model of damage prediction.

Abstract: The present paper aims to assess the accuracy of identification methods used in the evaluation of the flow stress relationship of tubular materials for hydroforming applications. Based on experimental data acquired from home designed and manufactured experimental tool and results collected from literature, flow stress parameters are determined using both analytical and inverse identification methods. The obtained results are coped to experimental measurements to validate the proposed approaches. It is shown from the analysis based on the comparative assessment of flow stress inferred from tube bulge test that, inverse parameter identification method is the appropriate methodology that contribute to a more accurate tube hydroforming characterization.